TY - JOUR
AB - Let P be a finite point set in the plane. A cordinary triangle in P is a subset of P consisting of three non-collinear points such that each of the three lines determined by the three points contains at most c points of P . Motivated by a question of Erdös, and answering a question of de Zeeuw, we prove that there exists a constant c > 0such that P contains a c-ordinary triangle, provided that P is not contained in the union of two lines. Furthermore, the number of c-ordinary triangles in P is Ω(| P |).
AU - Fulek, Radoslav
AU - Mojarrad, Hossein
AU - Naszódi, Márton
AU - Solymosi, József
AU - Stich, Sebastian
AU - Szedlák, May
ID - 793
JF - Computational Geometry: Theory and Applications
SN - 09257721
TI - On the existence of ordinary triangles
VL - 66
ER -